This month, Yo-Yo Ma turns 60. At a late-night BBC Prom last month, he played all six of Bach’s Cello Suites (the “Old Testament of the cello literature”, some people call them). He said he wanted to give “a quirky birthday present to myself”.

I remember well the concerts that another cellist, Mstislav Rostropovich, gave in 1987, in recognition of his own 60th birthday. Now that “Slava” is gone (he died in 2007), Ma is surely the most famous cellist in the world. He is also one of the most famous musicians — classical musicians—along with Plácido Domingo, Sir James Galway and a few others.

In America, he has been famous since he was a kid, impressing national television audiences with his phenomenal gifts. He studied at Juilliard and Harvard. He has made almost 100 albums — and because man cannot live on the Dvořák Concerto alone, he has played and recorded a great variety of music, from bluegrass to jazz to “world music”.

Ma is a fixture of the general American scene. Whenever there is an Occasion, and that Occasion calls for music, he is likely to be there. I’m talking about the season-opening concerts of our orchestras, of course. But also the Oscars, the Olympics, presidential inaugurations, funerals (Ted Kennedy, Steve Jobs). In 2010, Barack Obama gave Ma the Presidential Medal of Freedom. Also, Ma is a UN Messenger of Peace.

Onstage, he’s known for great ebullience and emotion. Reviewing a concerto performance, I wrote, “He took the stage with a hundred bows, smiles, waves, hugs — almost like an excited politician working the room.” And “when the concerto was finished, he was a veritable blizzard of hugs, bows, waves, kisses.” While playing, he can gyrate and mug, which is not to everyone’s taste.

What matters more, of course, is sound — and Ma owns one of the great string sounds of our time. It is rich, songful and beautiful. His playing is uneven, I have found. He’s on and off (like most of us). When he’s off, he tends to be sloppy and bathetic. After hearing a Sarabande, I wrote, “This was soupy, Romantic, swimming Bach, if it was Bach at all. It was a kind of musical goo — with hardly any spine, hardly any structure. A pianist would have blushed to play a Chopin nocturne that way.”

But when he’s on? Look out. Of many excellent and disciplined performances, I remember in particular a Shostakovich Concerto No 2. The composer, by the way, wrote this piece as a 60th-birthday present to himself — it contains autobiographical touches.

Like Rostropovich, Ma has been the cause of many cello commissions, which is to say, new music. And he has been a boost to many a cello career. Building on Pablo Casals, Slava and Jacqueline du Pré, Ma has mainstreamed the instrument. I know a professional cellist who, when he sees Ma, thanks him — for his own career.

The suddenly sexagenarian Ma is still youthful, still phenomenal, still wonderful. Don’t be surprised if he takes that to 100.